1. What is a Z-Score?

The Z-Score (standard score) measures how many standard deviations an element is from the mean. It's a dimensionless quantity used to compare different data points within a normal distribution.

2. How Does the Calculator Work?

The calculator uses the Z-Score formula:

Where:

• \( Z \) — Z-Score (dimensionless)
• \( x \) — Value to convert
• \( \mu \) — Mean of the population
• \( \sigma \) — Standard deviation of the population

Explanation: The formula calculates how far a data point is from the mean, measured in standard deviation units.

3. Importance of Z-Score

Details: Z-Scores are crucial in statistics for comparing different data points across different normal distributions, identifying outliers, and standardizing data for analysis.

4. Using the Calculator

Tips: Enter the value you want to convert, the population mean, and the population standard deviation. Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a Z-Score of 0 mean?
A: A Z-Score of 0 means the value is exactly equal to the mean of the population.

Q2: What is considered a "high" Z-Score?
A: Typically, Z-Scores beyond ±2 are considered unusual, and beyond ±3 are very unusual in a normal distribution.

Q3: Can Z-Scores be negative?
A: Yes, negative Z-Scores indicate values below the mean, while positive scores indicate values above the mean.

Q4: How is Z-Score different from T-Score?
A: T-Score is a modified Z-Score with a mean of 50 and standard deviation of 10, often used in educational testing.

Q5: What are practical applications of Z-Scores?
A: Used in quality control, finance (standardizing financial indicators), psychology (test scoring), and many other fields.